International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 15, Pages 777-788

A numerical study of effects of the axial stress on unsteady liquid pipeline flows

Masaji Watanabe,1 Yukio Kono,2 and Hiroshi Suito1

1Faculty of Environmental Science and Technology, Okayama University, Okayama, Tsushima 700-8530, Japan
2Faculty of Engineering, Tohoku Gakuin University, Tagajo 985-8537, Japan

Received 2 November 2002

Copyright © 2004 Masaji Watanabe et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the effects of the axial component of the shear stress on unsteady pipeline flows. We show that the axial component of the shear stress should be introduced in the modeling of unsteady flows, and as a numerical model, we propose a one-dimensional momentum equation in which a term containing the second derivative of the velocity with respect to space is introduced. The momentum equation and the continuity equation are converted into a system suitable for the application of upstream difference approximations. Numerical results are presented, and their correspondence with experimental results is examined to see how our model captures phenomena observed experimentally.